A London council is considering asking the education secretary, Michael Gove, to overturn one of Labour's key election pledges from 1997 and allow it to raise the limit on infant class sizes to more than 30 pupils.

Liberal Democrat-controlled Sutton council has contacted other local authorities in London to ask for support in an attempt to change the law restricting class sizes for the youngest children to 30.

A baby boom has put intense pressure on primary schools: the number of pupils is projected to increase by over half a million between 2010 and 2018. Figures from the Department for Education show the rise is steepest in London, where councils have built mobile classrooms in playgrounds to cope with the squeeze.

Labour legislated to limit infant class size to 30 pupils in 1998, fulfilling a commitment on its election pledge cards.

In a letter from its chief executive Niall Bolger to other London councils, Sutton council says this limit should be raised to allow 32 children in a class.

The council has already spent £7m funding additional classes for this September. It has been expanding primary schools for years, so "all easy options" to meet demand have been exhausted, it says.

Bolger's letter says: "We do not wish to eliminate all parameters for class size, but we consider 32 to be a pragmatic compromise between educational viability and financial prudency."

Sutton, which has 33 schools admitting infants, says that by adding two to each class it could provide all the extra places it needs. The chief executive says that this measure "would have provided over 130 additional places, the equivalent of almost five classes. This would, therefore have meant that no building programmes would have been required."

Bolger's letter acknowledges that all London councils face "unprecedented demand" for places.

He writes: "We seek support from other authorities, in taking forward the proposal, that infant class size should be increased to no more than 32."

After the council was contacted by journalists, Bolger issued a statement saying: "Increasing class sizes is not a Sutton council policy or something that has been discussed at a political level. My letter is a basic piece of research so that senior officers can present councillors with well-informed choices.

"There is a dreadful shortage of primary school places and we can't ignore the situation, especially when our schools, which are some of the best in the country, are attracting so many families."

Peter Walker, cabinet member for education for neighbouring Merton council, urged other local authorities to oppose the initiative.

He said: "Increasing class sizes in our schools at this time is short-sighted, will threaten school standards, is unfair to our children and will endanger our economic prospects."

Attempts to increase class sizes are likely to be unpopular with parents and teachers. However, research suggests that cutting class sizes is one of the least effective ways of improving children's performance.

Russell Hobby, general secretary of the National Association of Head Teachers said: "There are more important things than class size in terms of standards. There's evidence emerging to show that class size doesn't have the impact that we thought it did when we campaigned for it under Labour, compared with sheer high quality teaching or children spending more time in lessons. I'm sure it's more pleasant teaching smaller classes and it's more easy to keep under control."

The government has already announced extra funding to cope with the consequences of the baby boom.

The chancellor George Osborne announced in the autumn statement that an extra 40,000 school places would be provided in areas with the greatest demographic need, at a cost of £600m.

A Department for Education spokesman said: "The law remains clear that it is illegal for infant classes to exceed 30 pupils – no parent would want their child taught in a huge class.

"We're dealing with the impact of soaring birth rates on primary schools – doubling targeted investment at areas facing the greatest pressure on numbers to over £4bn in the next four years. We are building free schools in areas where there are place shortages and letting good schools expand without limits to meet demand from parents."